Abstract
This paper presents the nonlinear optimal feedback control for the deployment process of a tethered subsatellite model, which involves not only the usually addressed in-plane motion, but also the out-of-plane motion. The model also takes the uncertainties in the mass parameter, the perturbations in initial states, and the external disturbance forces into consideration from an engineering point of view. The proposed controller is on the basis of a shrinking horizon and online grid adaptation scheme. Even though the proposed feedback law is not analytically explicit, it is easy to determine it by using a rapid recomputation of the open-loop optimal control, which generates the initial guesses for controls by interpolating the results from the previous computation. The case studies in the paper well demonstrate the effectiveness, robustness, and dominant real-time merits of the proposed controller.
Similar content being viewed by others
References
Cosmo, M.L., Lorenzini, E.C.: Tethers in Space Handbook, 3rd edn. Smithsonian Astrophysical Observatory, Cambridge, Massachusetts (1997)
Barkow, B.A.: Chaos Control Strategy for the Deployment of a Tethered Satellite System. Dissertation, Vienna University of Technology, Vienna (2002)
Irvine, H.M., Caughey, T.K.: The linear theory of free vibrations of a suspended cable. Proc. R Soc. A 341(1626), 299–315 (1974)
Luongo, A., Rega, G., Vestroni, F.: Planar non-linear free vibrations of an elastic cable. Int. J. Non-Linear Mech. 19(1), 39–52 (1984)
Perkins, N.C., Mote Jr., C.D.: Three-dimensional vibration of traveling elastic cables. J. Sound Vib. 114(2), 325–340 (1987)
Luo, A.C.J., Mote Jr., C.D.: Equilibrium solutions and existence for traveling, arbitrarily sagged elastic cables. ASME J. Appl. Mech. 67(1), 148–154 (2000)
Rega, G.: Nonlinear vibrations of suspended cables —Part I: Modeling and analysis. Appl. Mech. Rev. 57(6), 443–478 (2004)
Barkow, B., Steindl, A., Troger, H.: A targeting strategy for the deployment of a tethered satellite system. IMA J. Appl. Math. 70(5), 626–644 (2005)
Steindl, A., Troger, H.: Optimal control of deployment of a tethered subsatellite. Nonlinear Dyn. 31(3), 257–274 (2003)
Williams, P., Trivailo, P.: On the optimal deployment and retrieval of tethered satellites. In: 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Reston, VA, AIAA-2005-4291
Jin, D.P., Hu, H.Y.: Optimal control of a tethered subsatellite of three degrees of freedom. Nonlinear Dyn. 46(1–2), 161–178 (2006)
Bainum, P., Kumar, V.K.: Optimal control of the shuttle-tethered-subsatellite system. Acta Astronaut. 7(12), 1333–1348 (1980)
Fujii, H.A., Anazawa, S.: Deployment/retrieval control of tethered subsatellite through an optimal path. J. Guid. Control Dyn. 17(6), 1292–1298 (1994)
Williams, P.: Application of pseudo-spectral methods for receding horizon control. J. Guid. Control Dyn. 27(2), 310–314 (2004)
Gläßel, H., Zimmermann, F., Brückner, S., Schöttle, U.M. et al.: Adaptive neural control of the deployment procedure for tether-assisted reentry. Aerospace Sci. Technol. 8(1), 73–81 (2004)
Sekhavat, P., Fleming, A., Ross, I.M.: Time-optimal nonlinear feedback control for the NPSAT1 spacecraft. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Monterey, vol. 2, pp. 843–850 (2005)
John, T.B.: Survey of numerical methods for trajectory optimization. J. Guid. Control Dyn. 21(2), 193–207 (1998)
Elnagar, G., Kazemi, M.A., Razzaghi, M.: The Legendre pseudo-spectral method for discretizing optimal control problems. IEEE Trans. Autom. Control 40(10), 1793–1796 (1995)
Ross, I.M., Fahroo, F.: Pseudo-spectral knotting methods for solving optimal control problems. J. Guid. Control Dyn. 27(3), 397–405 (2004)
Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Programming 106(1), 25–57 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wen, H., Jin, D.P. & Hu, H.Y. Optimal feedback control of the deployment of a tethered subsatellite subject to perturbations. Nonlinear Dyn 51, 501–514 (2008). https://doi.org/10.1007/s11071-007-9240-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-007-9240-3